Eliot Spitzer is telling friends his CNN co-host Kathleen Parker “will be gone within a week.” Relations between the ex-gov, who once called himself a “[bleep]ing steamroller,” and his conservative co-host are at an all-time low. A source said, “Spitzer thinks she’s holding him back. The ratings surged when she was out sick, and he anchored alone during the turmoil in Egypt. Only very few anchors have the power to wipe out a co-host, and Spitzer thinks he has it. CNN bosses are high on Spitzer, and he might get his own show. Kathleen has been weighing her options. There’s this sense of dread among middle management.” We’ve reported that Parker, a Pulitzer Prize-winning columnist, could be dumped due to lack of chemistry with Spitzer. But our source said, “She’s putting up a fight.” CNN President Ken Jautz recently said, “There have been lots of press reports that I am contemplating changes, but I’m not going to engage in any speculation.” A CNN rep declined to comment.